Answer
The solution to the system is ordered pair $(-\frac{44}{3},-\frac{7}{3})$.
Work Step by Step
Equation 1: $x = 5y - 3$
Equation 2: $x = 8y + 4$
Substitute equation 1 to equation 2:
$$5y - 3= 8y + 4$$
Add $3$ to both sides:
$$5y - 3+3= 8y + 4+3$$ $$5y= 8y+7$$
Subtract $8y$ from both sides:
$$5y-8y= 8y-8y+7$$ $$-3y=7$$
Divide both sides by $-3$:
$$\frac{-3y}{-3}=\frac{7}{-3}$$ $$y=-\frac{7}{3}$$
Substitute this value of $y$ to equation 1:
$$x = 5y - 3$$ $$x = 5(-\frac{7}{3}) - 3$$ $$x = -\frac{35}{3} - 3$$ $$x = -\frac{35}{3} - \frac{9}{3}$$ $$x =-\frac{44}{3}$$
Check using equation 2:
$$x = 8y + 4$$ $$-\frac{44}{3} = 8(-\frac{7}{3}) + 4$$ $$-\frac{44}{3} = -\frac{56}{3} + 4$$ $$-\frac{44}{3} = -\frac{56}{3} + \frac{12}{3}$$ $$-\frac{44}{3} =-\frac{44}{3}$$
Therefore, the solution to the system is ordered pair $(-\frac{44}{3},-\frac{7}{3})$.
